Evapotranspiration of Partially Vegetated Surfaces

surface two daily and hourly ET estimates in good agreement with the measured evapotranspiration. The performance of the S-W evaluated against two eddy covariance systems Ortega-Farias et a Cabernet This contains 23 chapters related to the modeling and simulation of evapotranspiration (ET) and remote sensing-based energy balance determination of ET. These areas are at the forefront of technologies that quantify the highly spatial ET from the Earth's surface. The topics describe mechanics of ET simulation from partially vegetated surfaces and stomatal conductance behavior of natural and agricultural ecosystems. Estimation methods that use weather based methods, soil water balance, the Complementary Relationship, the Hargreaves and other temperature-radiation based methods, and Fuzzy-Probabilistic calculations are described. A critical review describes methods used in hydrological models. Applications describe ET patterns in alpine catchments, under water shortage, for irrigated systems, under climate change, and for grasslands and pastures. Remote sensing based approaches include Landsat and MODIS satellite-based energy balance, and the common process models SEBAL, METRIC and S-SEBS. Recommended guidelines for applying operational satellite-based energy balance models and for overcoming common challenges are made.


Introduction
Latent heat flux equivalent to Evapotranspiration (ET) is the total amount of water lost via transpiration and evaporation from plant surfaces and the soil in an area where a crop is growing. Since 80-90% of precipitation received in semiarid and subhumid climates is commonly used in evapotranspiration, accurate estimations of ET are very important for hydrologic studies and crop water requirements. ET determination and modelling is not straightforward due to the natural heterogeneity and complexity of agricultural and natural land surfaces. In evapotranspiration modelling it is very common to represent vegetation assuming a single source of energy flux at an effective height within the canopy. However, when crops are sparse, the single source/sink of energy assumption in such models is not entirely satisfied. Improvements using multiple source models have been developed to estimate ET from crop transpiration and soil evaporation. Soil evaporation on partially vegetated surfaces over natural vegetation and orchards includes not only the soil under the canopy but also areas of bare soil between vegetation that contribute to ET. Soil evaporation can account for 25-45% of annual ET in agricultural systems. In irrigated agriculture, partially vegetated surfaces include fruit orchards (i.e. apples, oranges, vineyards, avocados, blueberries, and lemons among others), which cover a significant portion of the total area under irrigation. In semiarid regions, direct soil evaporation from sparse barley or millet crops can account for 30% to 60% of rainfall (Wallace et al., 1999). On a seasonal basis, sparse canopy soil evaporation can account for half of total rainfall (Lund & Soegaard, 2003). Allen (1990) estimated the soil evaporation under a sparse barley crop in northern Syria and found that about 70% of the total evaporation originated from the soil. Lagos (2008) estimated that under irrigated maize conditions soil evaporation accounted for around 26-36% of annual evapotranspiration. Under rain-fed maize conditions annual evaporation accounted for 36-39% of total ET. Under irrigated soybean the percentage was 41%, and under rainfed soybean conditions annual evaporation accounted for 45-47% of annual ET. Massman (1992) estimated that the soil contribution to total ET was about 30% for a short grass steppe measurement site in northeast Colorado. In a sparse canopy at the middle of the growing season, and after a rain event, more than 50% of the daily ET corresponds to directly soil evaporation (Lund & Soegaard, 2003). Soil evaporation can be maximized under frequent

ET modelling review
Evapotranspiration (ET) is the total amount of water lost via transpiration and evaporation from plant surfaces and the soil in an area where a crop is growing. Traditionally, ET from agricultural fields has been estimated using the two-step approach by multiplying the weather-based reference ET (Jensen et al., 1971;Allen et al., 1998 andASCE, 2002) by crop coefficients (Kc) to make an approximate allowance for crop differences. Crop coefficients are determined according to the crop type and the crop growth stage (Allen et al., 1998). However, there is typically some question regarding whether the crops grown compare with the conditions represented by the idealized Kc values (Parkes et al., 2005;Rana et al., www.intechopen.com 2005; Katerji & Rana, 2006;Flores, 2007). In addition, it is difficult to predict the correct crop growth stage dates for large populations of crops and fields (Allen et al., 2007). A second method is to make a one-step estimate of ET based on the Penman-Monteith (P-M) equation (Monteith, 1965), with crop-to-crop differences represented by the use of cropspecific values of surface and aerodynamic resistances (Shuttleworth, 2006). ET estimations using the one-step approach with the P-M model have been studied by several authors (Stannard, 1993;Farahani & Bausch, 1995;Rana et al., 1997;Alves & Pereira, 2000;Kjelgaard & Stockle, 2001;Ortega-Farias et al., 2004;Shuttleworth, 2006;Katerji & Rana, 2006;Flores, 2007;Irmak et al., 2008). Although different degrees of success have been achieved, the model has generally performed more satisfactorily when the leaf area index (LAI) is large (LAI>2). Results shows that the "big leaf" assumption used by the P-M model is not satisfied for sparse vegetation and crops with partial canopy cover. A third approach consists of extending the P-M single-layer model to a multiple-layer model (i.e. two layers in the Shuttleworth-Wallace (S-W) model (Shuttleworth-Wallace, 1985) and four layers in the Choudhury-Monteith (C-M) model (Choudhury & Monteith, 1988). Shuttleworth and Wallace (1985) combined a one-dimensional model of crop transpiration and a one-dimensional model of soil evaporation. Surface resistances regulate the heat and mass transfer in plant and soil surfaces, and aerodynamic resistances regulate fluxes between the surface and the atmospheric boundary layer. Several studies have evaluated the performance of the S-W model to estimate evapotranspiration (Farahani & Baush,1995;Stannard, 1993;Lafleur & Rouse, 1990;Farahani & Ahuja, 1996;Iritz et al. 2001;Tourula & Heikinheimo, 1998;Anadranistakis et al., 2000;Ortega-Farias et al., 2007). Field tests of the model have shown promising results for a wide range of both agricultural and non-agricultural vegetation. Farahani and Baush (1995) evaluated the performance of the P-M model and the S-W model for irrigated maize. Their main conclusion was that the Penman-Monteith model performed poorly when the leaf area index was less than 2 because soil evaporation was neglected in calculating surface resistance. Results of the S-W model were encouraging as it performed satisfactorily for the entire range of canopy cover. Stannard (1993) compared the P-M, S-W and Priestley-Taylor ET models for sparsely vegetated, semiarid rangeland. The P-M model was not sufficiently accurate (hourly r 2 =0.56, daily r 2 =0.60); however, the S-W model performs significantly better for hourly (r 2 =0.78) and daily data (r 2 =0.85). Lafleur and Rouse (1990) compared the S-W model with evapotranspiration calculated from the Bowen Ratio Energy Balance technique over a range of LAI from non-vegetated to fully vegetated conditions. The results showed that the S-W model was in excellent agreement with the measured evapotranspiration for hourly and day-time totals for all values of LAI. Using the potential of the S-W model to partition transpiration and evaporation, Farahani and Ahuja (1996) extended the model to include the effects of crop residues on soil evaporation by the inclusion of a partially covered soil area and partitioning evaporation between the bare and residue-covered areas. Iritz et al. (2001) applied a modified version of the S-W model to estimate evapotranspiration for a forest. The main modification consisted of a two-layer soil module, which enabled soil surface resistance to be calculated as a function of the wetness of the top soil. They found that the general seasonal dynamics of evaporation were fairly well simulated with the model. Tourula and Heikinheimo (1998) evaluated a modified version of the S-W model in a barley field. A modification of soil surface resistance and aerodynamic resistance, over two growing seasons, produced daily and hourly ET estimates in good agreement with the measured evapotranspiration. The performance of the S-W model was evaluated against two eddy covariance systems by Ortega-Farias et al. (2007) over a Cabernet www.intechopen.com Sauvignon vineyard. Model performance was good under arid atmospheric conditions with a correlation coefficient (r 2 ) of 0.77 and a root mean square error (RMSE) of 29 Wm -2 . Although good results have been found using the Shuttleworth-Wallace approach, the model still needs an estimation or measurement of soil heat flux (G) to estimate ET. Commonly, G is calculated as a fixed percentage of net radiation (Rn). Shuttleworth and Wallace (1985) estimated G as 20% of the net radiation reaching the soil surface. In the FAO56 method, Allen et al. (1998) estimated daily reference ET (ETr and ETo), assuming that the soil heat flux beneath a fully vegetated grass or alfalfa reference surface is small in comparison with Rn (i.e. G=0). For hourly estimations, soil heat flux was estimated as one tenth of the Rn during the daytime and as half of the Rn for the night time when grass was used as the reference surface. Similarly, G was assumed to be 0.04xRn for the daytime and 0.2xRn during the night time for an alfalfa reference surface. A more complete surface energy balance was presented by Choudhury and Monteith (1988). The proposed method developed a four-layer model for the heat budget of homogeneous land surfaces. The model is an explicit solution of the equations which define the conservation of heat and water vapor in a system consisting of uniform vegetation and soil. An important feature was the interaction of evaporation from the soil and transpiration from the canopy expressed by changes in the vapor pressure deficit of the air in the canopy. A second feature was the ability of the model to partition the available energy into sensible heat, latent heat, and soil heat flux for the canopy/soil system. Similar to Shuttleworth-Wallace (1985), the Choudhury-Monteith model included a soil surface resistance to regulate the heat and mass transfer at the soil surface. However, residue effects on the surface energy balance are not included in the model. Crop residue generally increases infiltration and reduces soil evaporation. Surface residue affects many of the variables that determine the evaporation rate. These variables include Rn, G, aerodynamic resistance and surface resistances to transport of heat and water vapor fluxes (Steiner, 1994;Horton et al., 1996;Steiner et al., 2000). Caprio et al. (1985) compared evaporation from three mini-lysimeters installed in bare soil and in a 14 and 28 cm tall standing wheat stubble. After nine days of measurements, evaporation from the lysimeter with stubble was 60% of the evaporation measured from bare soil. Enz et al. (1988) evaluated daily evaporation for bare soil and stubble-covered soil surfaces. Evaporation was always greater from the bare soil surface until it was dry, then evaporation was greater from the stubble covered-surface because more water was available. Evaporation from a bare soil surface has been described in three stages. An initial, energy-limited stage occurs when enough soil water is available to satisfy the potential evaporation rates. A second, falling rate stage is limited by water flow to the soil surface, while the third stage has a very low, nearly constant evaporative rate from very dry soil (Jalota & Prihar, 1998). Steiner (1989) evaluated the effect of residue (from cotton, sorghum and wheat) on the initial, energy-limited rate of evaporation. The evaporation rate relative to bare soil evaporation was described by a logarithmic relationship. Increasing the amount of residue on the soil surface reduced the relative evaporation rate during the initial stage. Bristow et al. (1986) developed a model to predict soil heat and water budgets in a soilresidue-atmosphere system. Results from application of the model indicate that surface residues decreased evaporation by roughly 36% compared with simulations from bare soil. With the recognition of the potential of multiple-layer models to estimate ET, a modified surface energy balance model (SEB) was developed by Lagos (2008) and Lagos et al. (2009) to include the effect of crop residue on evapotranspiration. The model relies mainly on the Schuttleworth- Wallace (1985) and Choudhury and Monteith (1988) approaches and has the potential to predict evapotranspiration for varying soil cover ranging from partially residue-covered soil to closed canopy surfaces. Improvements to aerodynamic resistance, surface canopy resistance and soil resistances for the transport of heat and water vapor were also suggested.

The SEB model
The modified surface energy balance (SEB) model has four layers (Figure 1), the first extended from the reference height above the vegetation and the sink for momentum within the canopy, a second layer between the canopy level and the soil surface, a third layer corresponding to the top soil layer and a lower soil layer where the soil atmosphere is saturated with water vapor. The soil temperature at the bottom of the lower level was held constant for at least a 24h period. The SEB model distributes net radiation (Rn), sensible heat (H), latent heat (E), and soil heat fluxes (G) through the soil/residue/canopy system. Horizontal gradients of the potentials are assumed to be small enough for lateral fluxes to be ignored, and physical and biochemical energy storage terms in the canopy/residue/soil system are assumed to be negligible. The evaporation of water on plant leaves due to rain, irrigation or dew is also ignored. The SEB model distributes net radiation (Rn) into sensible heat (H), latent heat (λE), and soil heat fluxes (G) through the soil-canopy system ( Figure 2). Total latent heat (λE) is the sum of latent heat from the canopy (λEc), latent heat from the soil (λEs) and latent heat from the residue-covered soil (λEr). Similarly, sensible heat is calculated as the sum of sensible heat from the canopy (Hc), sensible heat from the soil (Hs) and sensible heat from the residue covered soil (Hr). The total net radiation is divided into that absorbed by the canopy (Rnc) and the soil (Rns) and is given by Rn = Rnc + Rns. The net radiation absorbed by the canopy is divided into latent heat and sensible heat fluxes as Rnc = λEc +Hc. Similarly, for the soil Rns = Gos + Hs, where Gos is a conduction term downwards from the soil surface and is expressed as Gos = λEs + Gs, where Gs is the soil heat flux for bare soil. Similarly, for the residue-covered soil Rns = Gor + Hr where Gor is the conduction downwards from the soil covered by residue. The conduction is given by Gor = λEr + Gr where Gr is the soil heat flux for residue-covered soil. Total latent heat flux from the canopy/residue/soil system is the sum of the latent heat from the canopy (transpiration), latent heat from the soil and latent heat from the residue-covered soil (evaporation), calculated as: where fr is the fraction of the soil affected by residue. Similarly, the total sensible heat is given by: The differences in vapor pressure and temperature between levels can be expressed with an Ohm's law analogy using appropriate resistance and flux terms ( Figure 2). The sensible and latent heat fluxes from the canopy, from bare soil and soil covered by residue are expressed by (Shuttleworth & Wallace, 1985): where, ρ is the density of moist air, C p is the specific heat of air, is the psychrometric constant, T 1 is the mean canopy temperature, T 2 is the temperature at the soil surface, T b is the air temperature within the canopy, T 2r is the temperature of the soil covered by residue, r 1 is an aerodynamic resistance between the canopy and the air, r c is the surface canopy resistance, r 2 is the aerodynamic resistance between the soil and the canopy, r s is the resistance to the diffusion of water vapor at the top soil layer, r rh is the residue resistance to transfer of heat, r r is the residue resistance to the transfer of vapor acting in series with the soil resistance r s , e b is the vapor pressure of the atmosphere at the canopy level, e 1 * is the saturation vapor pressure in the canopy, e L * is the saturation vapor pressure at the top of the wet layer, and e Lr * is the saturation vapor pressure at the top of the wet layer for the soil covered by residue. Conduction of heat for the bare-soil and residue-covered surfaces are given by: where; r u and r L are resistance to the transport of heat for the upper and lower soil layers, respectively, T L and T Lr are the temperatures at the interface between the upper and lower layers for the bare soil and the residue-covered soil, and T m is the temperature at the bottom of the lower layer which was assumed to be constant on a daily basis.
www.intechopen.com Choudhury and Monteith (1988) expressed differences in saturation vapor pressure between points in the system as linear functions of the corresponding temperature differences. They found that a single value of the slope of the saturation vapor pressure, Δ, when evaluated at the air temperature, T a, gave acceptable results for the components of the heat balance. The vapor pressure differences were given by: e * −e * =∆• T −T The above equations were combined and solved to estimate fluxes. Details are provided by Lagos (2008). The solution gives the latent and sensible heat fluxes from the canopy as: The latent and sensible heat fluxes from the residue-covered soil are simulated with: λE = Rn •∆• r +r •r +ρ•C •[ e * −e • r +r +r +r + T −T •∆• r +r +r ] γ• r +r +r • r +r +r +r +∆•r • r +r +r Values for T b and e b are necessary to estimate latent heat and sensible heat fluxes. The values of the parameters can be expressed as: where, r ah is the aerodynamic resistance for heat transport, r aw is the aerodynamic resistance for water vapor transport, e a is the vapor pressure at the reference height, and e a * is the saturated vapor pressure at the reference height. Six coefficients (A 1 , A 2 , A 3 and B 1 , B 2 and B 3 ) are involved in these expressions. These coefficients depend on environmental conditions and other parameters. The expressions to compute the coefficients are given by (Lagos, 2008): •r γ• r +r • r +r +r +∆•r • r +r + f • Rn •∆• r +r •r γ• r +r +r • r +r +r +r +∆•r • r +r +r (16) A = ∆•r +γ• r +r + −f • r +r +r γ• r +r • r +r +r +∆•r • r +r + f • r +r +r +r γ• r +r +r • r +r +r +r +∆•r • r +r +r (17) A = −f • ∆• r +r γ• r +r • r +r +r +∆•r • r +r +f ∆• r +r +r γ• r +r +r • r +r +r +r +∆•r • r +r +r X = γ• r +r • r +r +r +∆•r • r +r r •∆+γ• r +r r •∆ and X = γ• r +r +r • r +r +r +r +∆•r • r +r +r r •∆+γ• r +r +r r •∆ These relationships define the surface energy balance model which is applicable to conditions ranging from closed canopies to surfaces with bare soil or those partially covered with residue. Without residue, the model is similar to that by Choudhury and Monteith (1988).

Determination of the SEB model parameters
In the following sections, the procedures to compute parameter values for the model are detailed. The parameters are as important as the formulation of the energy balance equations. Thom (1972) stated that heat and mass transfer encounter greater aerodynamic resistance than the transfer of momentum. Accordingly, aerodynamic resistances to heat (r ah ) and water vapor transfer (r aw ) can be estimated as:

Aerodynamic resistances
r =r +r and r =r +r (23) where r am is the aerodynamic resistance to momentum transfer, and r bh and r bw are excess resistance terms for heat and water vapor transfer. Shuttleworth and Gurney (1990) built on the work of Choudhury and Monteith (1988) to estimate r am by integrating the eddy diffusion coefficient over the sink of momentum in the canopy to a reference height z r above the canopy, giving the following relationship for r am : where k is the von Karman constant, u* is the friction velocity, z o is the surface roughness, d is the zero-plane displacement height, K h is the value of eddy diffusion coefficient at the top of the canopy, h is the height of vegetation, and  is the attenuation coefficient. A value of  = 2.5, which is typical for agricultural crops, was recommended by Shuttleworth and Wallace (1985) and Shuttleworth and Gurney (1990). Verma (1989) expressed the excess resistance for heat transfer as: where B -1 represents a dimensionless bulk parameter. Thom (1972) suggests that the product kB -1 equal approximately 2 for most arable crops. Excess resistance was derived primarily from heat transfer observations (Weseley & Hicks 1977). Aerodynamic resistance to water vapor was modified by the ratio of thermal and water vapor diffusivity: where, k 1 is the thermal diffusivity and D v is the molecular diffusivity of water vapor in air. Similarly, Shuttleworth and Gurney (1990) expressed the aerodynamic resistance (r 2 ) by integrating the eddy diffusion coefficient between the soil surface and the sink of momentum in the canopy to yield: where z o ' is the roughness length of the soil surface. Values of surface roughness (z o ) and displacement height (d) are functions of leaf area index (LAI) and can be estimated using the expressions given by Shaw and Pereira (1982). The diffusion coefficients between the soil surface and the canopy, and therefore the resistance for momentum, heat, and vapor transport are assumed equal although it is recognized that this is a weakness in the use of the K theory to describe through-canopy transfer (Shuttleworth & Gurney, 1990). Stability is not considered.

Canopy resistances
The mean boundary layer resistance of the canopy r 1 , for latent and sensible heat flux, is influenced by the surface area of vegetation (Shuttleworth & Wallace, 1985): where r b is the resistance of the leaf boundary layer, which is proportional to the temperature difference between the leaf and surrounding air divided by the associated flux (Choudhury & Monteith, 1988). Shuttleworth and Wallace (1985) noted that resistance r b exhibits some dependence on in-canopy wind speed, with typical values of 25 s m -1 . Shuttleworth and Gurney (1990) represented r b as: where w is the representative leaf width and u h is the wind speed at the top of the canopy. This resistance is only significant when acting in combination with a much larger canopy surface resistance, and Shuttleworth and Gurney (1990) suggest that r 1 could be neglected for foliage completely covering the ground. Using r b = 25 s m -1 with an LAI = 4, the corresponding canopy boundary layer resistance is r 1 = 3 s m -1 . Canopy surface resistance, r c , can be calculated by dividing the minimum surface resistance for a single leaf (r l ) by the effective canopy leaf area index (LAI). Five environmental factors have been found to affect stomata resistance: solar radiation, air temperature, humidity, CO 2 concentration and soil water potential (Yu et al., 2004). Several models have been developed to estimate stomata conductance and canopy resistance. Stannard (1993) estimated r c as a function of vapor pressure deficit, leaf area index, and solar radiation as: where LAI max is the maximum value of leaf area index, VPD a is vapor pressure deficit, Rad is solar radiation, Rad max is the maximum value of solar radiation (estimated at 1000 W m -2 ) and C 1 , C 2 and C 3 are regression coefficients. Canopy resistance does not account for soil water stress effects.

Soil resistances
Farahani and Bausch (1995), Anadranistakis et al. (2000) and Lindburg (2002) found that soil resistance (r s ) can be related to volumetric soil water content in the top soil layer. Farahani and Ahuja (1996) found that the ratio of soil resistance when the surface layer is wet relative to its upper limit depends on the degree of saturation (θ/θ s ) and can be described by an exponential function as: where L t is the thickness of the surface soil layer, τ s is a soil tortuosity factor, D v is the water vapor diffusion coefficient and ∅ is soil porosity, θ is the average volumetric water content in the surface layer, θ s is the saturation water content, and is a fitting parameter. Measurements of θ from the top 0.05 m soil layer were more effective in modeling r s than θ for thinner layers. Choudhury and Monteith (1988) expressed the soil resistance for heat flux (r L ) in the soil layer extending from depth L t to L m as: where K is the thermal conductivity of the soil. Similarly, the corresponding resistance for the upper layer (r u ) of depth L t and conductivity K' as:

Residue resistances
Surface residue is an integral part of many cropping systems. Bristow and Horton (1996) showed that partial surface mulch cover can have dramatic effects on the soil physical environment. The vapor conductance through residue has been described as a linear function of wind speed. Farahani and Ahuja (1996) used results from Tanner and Shen (1990) to develop the resistance of surface residue (r r ) as: where L r is residue thickness, τ r is residue tortuosity, D v is vapor diffusivity in still air, ∅ is residue porosity and u 2 is wind speed measured two meters above the surface. Due to the porous nature of field crop residue layers, the ratio τ r /∅ is about one (Farahani & Ahuja, 1996). Similar to the soil resistance, Bristow and Horton (1996) and Horton et al. (1996) expressed the resistance of residue for heat transfer, r rh , as: where K r is the residue thermal conductivity. The fraction of the soil covered by residue (f r ) can be estimated using the amount and type of residue (Steiner et al., 2000). The soil covered by residue and the residue thickness are estimated using the expressions developed by Gregory (1982).

SEB model inputs
Inputs required to solve multiple layer models (i.e. Shuttleworth and Wallace (1985), Choudhury and Monteith (1988) and Lagos (2008) models) are net radiation, solar radiation, air temperature, relative humidity, wind speed, LAI, crop height, soil texture, soil temperature, soil water content, residue type, and residue amount. In particular, net radiation, leaf area index, soil temperatures and residue amount are variables rarely measured in the field, other than at research sites. Net radiation and soil temperature models can be incorporated into surface energy balance models to predict evapotranspiration from environmental variables typically measured by automatic weather stations. Similar to the Shuttleworth and Wallace (1985) and Choudhury and Monteith (1988) models, measurements of net radiation and estimations of net radiation absorbed by the canopy are necessary for the SEB model. Beer's law is used to estimate the penetration of radiation through the canopy and estimates the net radiation reaching the surface (Rn s ) as:

Rn =Rn•exp −C •LAI)
where Cext is the extinction coefficient of the crop for net radiation. Consequently, net radiation absorbed by the canopy (Rnc) can be estimated as Rnc = Rn -Rn s .

SEB model evaluation
An irrigated maize field site located at the University of Nebraska Agricultural Research and Development Center near Mead, NE (41 o 09'53.5"N, 96 o 28'12.3"W, elevation 362 m) was used for model evaluation. This site is a 49 ha production field that provides sufficient upwind fetch of uniform cover required for adequately measuring mass and energy fluxes using eddy covariance systems. The area has a humid continental climate and the soil corresponds to a deep silty clay loam ). The field has not been tilled since 2001. Detailed information about planting densities and crop management is provided by Verma et al. (2005) and Suyker and Verma (2009).
Soil water content was measured continuously at four depths (0.10, 0.25, 0.5 and 1.0 m) with Theta probes (Delta-T Device, Cambridge, UK). Destructive green leaf area index and biomass measurements were taken bi-monthly during the growing season. The eddy covariance measurements of latent heat, sensible heat and momentum fluxes were made using an omnidirectional three dimensional sonic anemometer (Model R3, Gill Instruments Ltd., Lymington, UK ) and an open-path infrared CO 2 /H 2 O gas analyzer system (Model LI7500, Li-Cor Inc, Lincoln, NE). Fluxes were corrected for sensor frequency response and variations in air density. More details of measurements and calculations are given in Verma et al. (2005). Air temperature and humidity were measured at 3 and 6 meters (Humitter 50Y, Vaisala, Helsinki, Finland), net radiation at 5.5 m (CNR1, Kipp and Zonen, Delft, NLD) and soil heat flux at 0.06 m (Radiation and Energy Balance Systems Inc, Seattle, WA). Soil temperature was measured at 0.06, 0.1, 0.2 and 0.5 m depths (Platinum RTD, Omega Engineering, Stamford, CT). More details are given in Verma et al. (2005) and Suyker and Verma ( 2009). Evapotranspiration predictions from the SEB model were compared with eddy covariance flux measurements during 2003 for an irrigated maize field. To evaluate the energy balance closure of eddy covariance measurements, net radiation was compared against the sum of latent heat, sensible heat, soil heat flux and storage terms. Storage terms include soil heat storage, canopy heat storage, and energy used in photosynthesis. Storage terms were calculated by Suyker and Verma (2009) following Meyers and Hollinger (2004). During these days, the regression slope for energy balance closure was 0.89 with a correlation coefficient of r 2 = 0.98. For model evaluation, 15 days under different LAI conditions were selected to initially test the model, however further work is needed to test the model for entire growing seasons and during longer periods. Hourly data for three 5-day periods with varying LAI conditions (LAI = 0, 1.5 and 5.4) were used to compare measured ET to model predictions. Input data of the model included hourly values for: net radiation, air temperature, relative humidity, soil temperature at 50 cm, wind speed, solar radiation and soil water content. During the first 5-day period, which was prior to germination, the maximum net radiation ranged from 240 to 720 W m -2 , air temperature ranged from 10 to 30°C, soil temperature was fairly constant at 16°C and wind speed ranged from 1 to 9 m s -1 but was generally less than 6 m s -1 (Figure 3). Soil water content in the evaporation zone averaged 0.34 m 3 m -3 and the residue density was 12.5 ton/ha on June 6, 2003. Precipitation occurred on the second and fifth days, totaling 17 mm. Evapotranspiration estimated with the SEB model and measured using the eddy covariance system is given in Figure 4. ET fluxes were the highest at midday on June 6, reaching approximately 350 W m -2 . The lowest ET rates occurred on the second day. Estimated ET tracked measured latent heat fluxes reasonably well. Estimates were better for days without precipitation than for days when rainfall occurred. The effect of crop residue on evaporation from the soil is shown in Figure 4 for this period. Residue reduced cumulative evaporation by approximately 17% during this five-day period. Evaporation estimated with the SEB model on June 6 and 9 was approximately 3.5 mm/day, totaling approximately half of the total evaporation for the five days. During the second five-day period, when plants partially shaded the soil surface (LAI = 1.5), the maximum net radiation ranged from 350 to 720 W m -2 and air temperature ranged from 10 to 33°C ( Figure 5). The soil temperature was nearly constant at 20°C. Wind speed ranged from 0.3 to 8 m s -1 but was generally less than 6 m s -1 . The soil water content was about 0.31 m 3 m -3 and the residue density was 12.2 ton/ha on June 24, 2003. Precipitation totaling 3mm occurred on the fifth day. The predicted rate of ET estimated with the SEB model was close to the observed data ( Figure 6). Estimates were smaller than measured values for June 24, which was the hottest and windiest day of the period. The ability of the model to partition ET into evaporation and transpiration for partial canopy conditions is also illustrated in Figure 6. Evaporation from the soil represented the majority of the water used during the night, and early or late in the day. During the middle of the day transpiration represented approximately half of the hourly ET flux. Fig. 3. Environmental conditions during a five-day period without canopy cover for net radiation (Rn), air temperature (T a ), soil temperature (T m ), precipitation (Prec.), vapor pressure deficit (VPD), and wind speed (u). The last period represents a fully developed maize canopy that completely shaded the soil surface. The crop height was 2.3 m and the LAI was 5.4. Environmental conditions for the period are given in Figure 7. The maximum net radiation ranged from 700 to 740 W m -2 and air temperature ranged from 15 to 36 ºC during the period. Soil temperature was fairly constant during the five days at 21.5°C and wind speed ranged from 0.3 to 4 m s -1 . The soil water content was about 0.25 m 3 m -3 and the residue density was 11.8 ton/ha on July 16, 2003. Precipitation totaling 29 mm occurred on the third day. Observed and predicted ET fluxes agreed for most days with some differences early in the morning during the first day and during the middle of several days (Figure 8). Transpiration simulated with the SEB model was nearly equal to the simulated ET for the period as evaporation rates from the soil was very small. Fig. 4. Evapotranspiration estimated by the Surface Energy Balance (SEB) model and measured by an eddy covariance system and simulated cumulative evaporation from bare and residue-covered soil for a period without plant canopy cover.    Hourly measurements and SEB predictions for the three five-day periods were combined to evaluate the overall performance of the model (Figure 9). Results show variation about the 1:1 line; however, there is a strong correlation and the data are reasonably well distributed about the line. Modeled ET is less than measured for latent heat fluxes above 450 W m -2 . The model underestimates ET during hours with high values of vapor pressure deficit ( Figure 6 and 8), this suggests that the linear effect of vapor pressure deficit in canopy resistance estimated with equation (30) produce a reduction on ET estimations. Further work is required to evaluate and explore if different canopy resistance models improve the performance of ET predictions under these conditions. Various statistical techniques were used to evaluate the performance of the model. The coefficient of determination, Nash-Sutcliffe coefficient, index of agreement, root mean square error and the mean absolute error were used for model evaluation (Legates & McCabe 1999;Krause et al., 2005;Moriasi et al., 2007;Coffey et al. 2004). The coefficient of determination was 0.92 with a slope of 0.90 over the range of hourly ET values. The root mean square error was 41.4 W m -2 , the mean absolute error was 29.9 W m -2 , the Nash-Sutcliffe coefficient was 0.92 and the index of agreement was 0.97. The statistical parameters show that the model represents field measurements reasonably well. Similar performance was obtained for daily ET estimations (Table 1). Analysis is underway to evaluate the model for more conditions and longer periods. Simulations reported here relied on literature-reported parameter values. We are also exploring calibration methods to improve model performance.

The modified SEB model for Partially Vegetated surfaces (SEB-PV)
Although good performance of multiple-layer models has been recognized, multiple-layer models estimate more accurate ET values under high LAI conditions. Lagos (2008) evaluated the SEB model for maize and soybean under rainfed and irrigated conditions; results indicate that during the growing season, the model more accurately predicted ET after canopy closure (after LAI=4) than for low LAI conditions. The SEB model, similar to S-W and C-M models, is based on homogeneous land surfaces. Under low LAI conditions, the land surface is partially covered by the canopy and soil evaporation takes place from soil below the canopy and areas of bare soil directly exposed to net radiation. However, in multiple-layer models, evaporation from the soil has been only considered below the canopy and hourly variations in the partitioning of net radiation between the canopy and the soil is often disregarded. Soil evaporation on partially vegetated surfaces & inorchards and natural vegetation include not only soil evaporation beneath the canopy but also evaporation from areas of bare soil that contribute directly to total ET. Recognizing the need to separate vegetation from soil and considering the effect of residue on evaporation, we extended the SEB model to represent those common conditions. The modified model, hereafter the SEB-PV model, distributes net radiation (Rn), sensible heat (H), latent heat (E), and soil heat fluxes (G) through the soil/residue/canopy system. Similar to the SEB model, horizontal gradients of the potentials are assumed to be small enough for lateral fluxes to be ignored, and physical and biochemical energy storage terms in the canopy/residue/soil system are assumed to be negligible. The evaporation of water on plant leaves due to rain, irrigation or dew is also ignored.
The SEB-PV model has the same four layers described previously for SEB ( Figure 10):the first extended from the reference height above the vegetation and the sink for momentum within the canopy, a second layer between the canopy level and the soil surface, a third layer corresponding to the top soil layer and a lower soil layer where the soil atmosphere is saturated with water vapor. Total latent heat (E) is the sum of latent heat from the canopy (Ec), latent heat from the soil (Es) beneath the canopy, latent heat from the residue-covered soil (Er) beneath the canopy, latent heat from the soil (Ebs) directly exposed to net radiation and latent heat from the residue-covered soil (Ebr) directly exposed to net radiation.
Where fr is the fraction of the soil affected by residue and Fv is the fraction of the soil covered by vegetation. Similarly, sensible heat is calculated as the sum of sensible heat from the canopy (Hc), sensible heat from the soil (Hs) and sensible heat from the residue covered soil (Hr), sensible heat from the soil (bs) directly exposed to net radiation and latent heat from the residue-covered soil (Hbr) directly exposed to net radiation.

H = [Hc + Hs − fr + Hr fr ] Fv + [ Hbs − fr + Hbr fr] − Fv
For the fraction of the soil covered by vegetation, the total net radiation is divided into that absorbed by the canopy (Rnc) and the soil beneath the canopy (Rns) and is given by Rn = Rnc + Rns. The net radiation absorbed by the canopy is divided into latent heat and sensible heat fluxes as Rnc = Ec + Hc. Similarly, for the soil Rns = Gos + Hs, where Gos is a conduction term downwards from the soil surface and is expressed as Gos = Es + Gs, where Gs is the soil heat flux for bare soil. Similarly, for the residue covered soil Rns = Gor + Hr where Gor is the conduction downwards from the soil covered by residue. The conduction is given by Gor = Er + Gr where Gr is the soil heat flux for residue-covered soil. For the area without vegetation, total net radiation is divided into latent and sensible heat fluxes as Rn = Ebs +Ebr + Hbs + Hbr. The differences in vapor pressure and temperature between levels can be expressed with an Ohm's law analogy using appropriate resistance and flux terms ( Figure 10). Latent and sensible flux terms with in the resistance network were combined and solved to estimate total fluxes. The solution gives the latent and sensible heat fluxes from the canopy, the soil beneath the canopy and the soil covered by residue beneath the canopy similar to equations (9), (10), (11), (12) and (13). The new expressions for latent heat flux of bare soil and soil covered by residue, both directly exposed to net radiation are: For bare soil: λE = R •∆• r •r +ρ•C • e * −e •r +r +r + T −T •∆• r +r γ• r +r • r +r +r +∆•r • r +r For residue covered soil: • r 2b + r s + r r • r u + r L + r 2b + r rh +∆•r L • r u + r 2b + r rh These relationships define the surface energy balance model, which is applicable to conditions ranging from closed canopies to surfaces partially covered by vegetation. If Fv = 1 the model SEB-PV is similar to the original SEB model and with Fv=1 without residue, the model is similar to that by Choudhury and Monteith (1988). www.intechopen.com

Model resistances
Model resistances are similar to those described by the SEB model; however, a new aerodynamic resistance (r 2b ) for the transfer of heat and water flux is required for the surface without vegetation. The aerodynamic resistance between the soil surface and Zm (r 2b ) could be calculated by assuming that the soil directly exposed to net radiation is totally unaffected by adjacent vegetation as: According to Brenner and Incoll (1997), actual aerodynamic resistance (r 2b ) will vary between r as for Fv=0 and r 2 when the fractional vegetative cover Fv=1. The form of the functional relationship of this change is not known, r 2b was varied linearly between r as and r 2 as:

Model inputs
The proposed SEB-PV model requires the same inputs of the SEB model plus the fraction of the surface covered by vegetation (Fv).

Sensitivity analysis
A sensitivity analysis was performed to evaluate the response of the SEB model to changes in resistances and model parameters. Meteorological conditions, crop characteristics and soil/residue characteristics used in these calculations are given in Table 2. Such conditions are typical for midday during the growing season of maize in southeastern Nebraska. The sensitivity of total latent heat from the system was explored when model resistances and model parameters were changed under different LAI conditions. The effect of the changes in model parameters and resistances were expressed as changes in total ET (λE) and changes in the crop transpiration ratio. The transpiration ratio is the ratio between crop transpiration (Ec) over total ET (transpiration ratio= Ec / E).
The response of the SEB model was evaluated for three values of the extinction coefficient (Cext = 0.4, 0.6 and 0.8), three conditions of vapor pressure deficit (VPDa = 0.5 kPa, 0.1 kPa and 0.25 kPa) three soil temperatures (T m =21°C, 0.8xT m =16.8 °C and 1.2xT m =25.2 °C ) ( Figure  11), changes in the parameterization of aerodynamic resistances (the attenuation coefficient, = 1, 2.5 and 3.5), the mean boundary layer resistance, r b (±40% ) the crop height, h (±30%)), selected conditions for the soil surface resistance, r s ( 0, 227, and 1500 s m -1 ) (Figure 12), four values for residue resistance, r r (0, 400, 1000, and 2500 s m -1 ), and changes of ±30% in surface canopy resistance, r c ( Figure 13). In general, the sensitivity analysis of model resistances showed that simulated ET was most sensitive to changes in surface canopy resistance for LAI > 0.5 values, and soil surface resistance and residue surface resistance for small LAI values (LAI < ~3). The model was less sensitive to changes in the other parameters evaluated. Wind speed at two meters above the surface (m s -1 ). K Thermal conductivity of the soil, upper layer (W m -1 o C -1 ). K' Thermal conductivity of the soil, lower layer (W m -1 o C -1 ). K r Thermal conductivity of the residue layer (W m -1 o C -1 ). C ext Extinction coefficient. Fv Fraction of the soil covered by vegetation. H bs Sensible heat from the soil (W m -2 ). H br Latent heat from the residue-covered soil (W m -2 ).